If y=y(x) is the solution curve of the differential equation (x²-4) d y-(y²-3 y) d x=0, x>2, y(4)=3/2 and the slope of the curve is never zero, then the value of y(10) equals:

Differential Equations: JEE Main 2024 Mathematics question

JEE Main 2024 · 27 Jan, Evening shift · Q3642

JEE Main 202427 Jan, Evening shiftMathematicsMediumDifferential Equations163× since 2002

y=y(x)

is the solution curve of the differential equation

\left(x^2-4\right) \mathrm{d} y-\left(y^2-3 y\right) \mathrm{d} x=0, x>2, y(4)=\frac{3}{2}

and the slope of the curve is never zero, then the value of

y(10)

equals :

JEE Main 2024 · 27 Jan, Evening shift · Q3642

JEE Main 202427 Jan, Evening shiftMathematicsMediumDifferential Equations163× since 2002

y=y(x)

is the solution curve of the differential equation

\left(x^2-4\right) \mathrm{d} y-\left(y^2-3 y\right) \mathrm{d} x=0, x>2, y(4)=\frac{3}{2}

and the slope of the curve is never zero, then the value of

y(10)

equals :